Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽₁−𝐽₂ 𝑞-state Potts model (𝑞=2 is known as the Ising model) stands as the simplest framework for frustrated magnets, but had remained unsolved generally for 50 years. Here, we present an exact analytic solution for arbitrary 𝑞 by block-diagonalizing the original 𝑞²×𝑞² transfer matrix into a simple 2×2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞=3 case. Furthermore, by matching relevant subspaces, we exactly map the model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽₂ acts as the nearest-neighbor interaction and 𝐽₁ as an effective magnetic field. The existence of infinitely many exact mappings raises the general question of to what extent the frustration induced in an external magnetic field corresponds to the geometrical frustration arising spontaneously from competing spin–spin interactions. Such correspondence can facilitate not only fundamental research but also material design. The work demonstrates that AI can be successfully used as a research partner for scientific discovery -- even in theoretical physics, which is deeply grounded in mathematics.